Joseph Taylor Robinson was the popular, long-time US Senator from Arkansas, that is depicted on the 1936 Arkansas Statehood Centennial - Robinson Type half dollar. He first served in Congress from March 1903 to January 1913 as a US Representative from Arkansas. He resigned to serves briefly as Arkansas Governor, then returned to Congress as a US Senator from Arkansas from 1913 until his death in 1937 (63rd to 75th Congresses).
This long-term service to the people of Arkansas, and his popularity among his colleagues, made his portrait a natural design consideration when Congress passed a bill granting the Arkansas Centennial Commission a second design for its commemorative half dollar. But his portrait was not the first design considered.
The first design theme to be explored

involved the Spanish Explorer/Conquistador Hernando de Soto. In a letter written by Augustus W. Parke, Executive Secretary of the Centennial Commission, and addressed to the Commission on Fine Arts, Parke stated the Commission was considering for the new coin a reverse design that depicted "one side of a coin Ferdinand De Soto is supposed to have presented to an Indian woman in Arkansas during his exploration of this State." (A silver Spanish "piece of eight" perhaps?)
Hernando de Soto
(Image Credit: Library of Congress, Prints and Photographs Division. Public Domain.)De Soto is considered to be the first European to explore present-day Arkansas. His expedition explored the southeast region of the future US between 1539 and 1543 (de Soto died during the expedition in 1542); the expedition was in search of gold and other riches (de Soto was hoping to repeat his successes from South America).
He landed first in Florida (near present-day Tampa Bay) and then moved north into Georgia and South/North Carolina, west into Tennessee and then south through Georgia and into Alabama. Further explorations found de Soto's expedition moving into Mississippi and Arkansas. De Soto never found the riches he sought. (Note: All State name references reflect present-day political boundaries.)
The de Soto expedition encountered many Native American communities during its explorations. Sometimes these encounters were friendly, other times they were harsh and violent with the more modern weaponry of the Spanish prevailing. Hernando de Soto died, presumably of a fever, in Arkansas in 1542. The expedition spent - before and after de Soto's death combined - approximately one year in Arkansas before traveling down the Mississippi River and making its way to Mexico.
It would have made for a history-rich coin if the de Soto theme had been pursued, but modern political pressures convinced the Commission that Robinson was the "preferred" choice. Many of today's collectors are not aware of "what might have been."
1936 Arkansas Statehood Centennial Half Dollar - Senator Joseph T. Robinson Type

For other of my posts about commemorative coins and medals, including more Arkansas Statehood Centennial half dollar stories, see:
Commems Collection.